BACK UP VELOCITY ESTIMATE FOLLOWING AIR DATA SYSTEM FAILURE (PROJECT HAVE VEST) DECEMBER 2007 FINAL TECHNICAL INFORMATION MEMORANDUM

Transcription

1 Project Have VEST AFFTC-TIM September 2007 Edwards Air Force Base Air Force Flight Test Center BACK UP VELOCITY ESTIMATE FOLLOWING AIR DATA SYSTEM FAILURE (PROJECT HAVE VEST) A F F Maj Scott McLaren Project Manager/Project Test Pilot Sqn Ldr Sreeram Jayashankar Project Test Pilot Maj William Rothermel Project Test Pilot Capt Corey Beaverson Project Flight Test Engineer Capt Donny Powers Project Flight Test Engineer T C DECEMBER 2007 FINAL TECHNICAL INFORMATION MEMORANDUM Approved for public release; distribution is unlimited. AIR FORCE FLIGHT TEST CENTER EDWARDS AIR FORCE BASE, CALIFORNIA AIR FORCE MATERIAL i COMMAND UNITED STATES AIR FORCE

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3 Form Approved REPORT DOCUMENTATION PAGE OMB No Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports ( ), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE 2. REPORT TYPE 3. DATES COVERED (From To) December 2007 Final Technical Information Memorandum 9 to 21 September TITLE AND SUBTITLE 5a. CONTRACT NUMBER Back Up Velocity Estimate Following Air Data System Failure 6. AUTHOR(S) McLaren, Scott A., Major, USAF Beaverson, Corey A., Captain, USAF Jayashankar, Sreeram, Squadron Leader, IAF Powers, Donald W., Captain, USAF Rothermel, William H., Major, USMC 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Air Force Flight Test Center 412th Test Wing USAF Test Pilot School 220 South Wolfe Ave. Edwards AFB CA PERFORMING ORGANIZATION REPORT NUMBER AFFTC-TIM SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR S ACRONYM(S) Air Force Institute of Technology Major Paul Blue 2950 Hobson Way WPAFB, OH DISTRIBUTION / AVAILABILITY STATEMENT Approved for public release; distribution is unlimited. 11. SPONSOR/MONITOR S REPORT NUMBER(S) 13. SUPPLEMENTARY NOTES CA: Air Force Flight Test Center, Edwards AFB CA CC: ABSTRACT This report presents the results of Project Have VEST, a limited evaluation of a back up velocity estimate following air data system failure. This test program demonstrated the potential of the VEST algorithm to provide an airspeed estimate using aircraft last known state and flight control computer accelerations and rates. The USAF Test Pilot School (TPS), Class 07A, conducted six flight tests totaling 11.3 hours at Edwards AFB, California, from 9 to 21 Sep All test objectives were met. 15. SUBJECT TERMS Have VEST Velocity Estimation Calspan Variable Stability Learjet Learjet N101VS In-flight Simulator Flight Test Ground Test Gain Scheduling Air Data System Failure Matlab Simulink 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT a. REPORT UNCLASSIFIED b. ABSTRACT UNCLASSIFIED c. THIS PAGE UNCLASSIFIED SAME AS REPORT iii 18. NUMBER 19a. NAME OF RESPONSIBLE PERSON OF PAGES Maj Paul Blue 56 19b. TELEPHONE NUMBER (include area code) (937) Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std

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5 EXECUTIVE SUMMARY This final technical information memorandum presents the test procedures and results for the Have VEST Test Management Project (TMP). The Have VEST (Velocity Estimate) Test Team performed flight tests to characterize the performance of a velocity estimator algorithm developed as part of an Air Force Institute of Technology (AFIT) Master s Thesis. The Commandant of USAF Test Pilot School (TPS) directed this program at the request of the Department of Aeronautics and Astronautics (ENY), Air Force Institute of Technology (AFIT). All testing was accomplished under TPS Job Order Number M07C0700 using the Calspan Variable Stability Learjet (N101VS) aircraft. A total of 11.3 hours of flight test were flown during 6 test sorties in the R-2508 complex during September 2007 to accomplish the test objectives. Following air data system failure, all sensors providing airspeed, altitude, temperature, angle of attack, and pressure readings would be unavailable for use by aircraft systems. Currently, flight control system operation following air data system failure is accomplished using standby gain settings. While standby gains provide necessary information for continued safe flight in recovering the aircraft, they do not provide an optimal gain schedule to allow continuation of the mission. The VEST algorithm was used to continuously estimate true airspeed following a complete air data system failure. The algorithm provided an estimate of the lost air data information. The algorithm estimated flight conditions were used to schedule stick command gain and to display airspeed and altitude information in the cockpit. The true and calibrated airspeed error profiles were determined to be independent of aircraft maneuvers or speeds. Individual error profiles were variable with time, but magnitudes of error were less than the current standby gain scheduling that assumes constant airspeeds. The average true airspeed error was on the order of 12 knots (21 feet per second), non-divergent and minimally variable. Similarly the average calibrated airspeed error was on the order of 10 knots (17 feet per second). The results of this test demonstrate the potential of this type of airspeed estimation as a back up system following air data failures, and warrants continued research. v

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7 TABLE OF CONTENTS EXECUTIVE SUMMARY...v LIST OF ILLUSTRATIONS... viii LIST OF TABLES... viii INTRODUCTION...1 Background... 1 Program Chronology... 1 Test Item Description... 2 Test Aircraft...2 Test Objectives... 3 TEST AND EVALUATION...5 General... 5 Integration of Velocity Estimate (VEST) Algorithm in a Ground Test... 5 Accuracy of the VEST Algorithm Inertial Speed during Taxi... 7 Airborne Accuracy of the VEST Algorithm Inertial Estimate... 9 Airborne Accuracy of the VEST Algorithm Wind Estimate Utility of the VEST Algorithm in Operational Maneuvers Airborne Accuracy of the VEST Algorithm Airspeed Estimate CONCLUSIONS AND RECOMMENDATIONS...23 Integration of VEST Algorithm in a Ground Test Accuracy of the VEST Algorithm Inertial Speed during Taxi Airborne Accuracy of the VEST Algorithm Inertial Estimate Airborne Accuracy of the VEST Algorithm Wind Estimate Utility of the VEST Algorithm in Operational Maneuvers Airborne Accuracy of the VEST Algorithm Airspeed Estimate REFERENCES...25 APPENDIX A DETAILED TEST ARTICLE DESCRIPTION A-1 APPENDIX B TECHNICAL DATA ANALYSIS... B-1 APPENDIX C FLIGHT TEST MANEUVER DESCRIPTIONS.. C-1 APPENDIX D PILOT COMMENT ANALOG SCALE... D-1 APPENDIX E PLOTS OF RESULTS... E-1 APPENDIX F LIST OF ACRONYMS.. F-1 APPENDIX G PILOT IN LOOP OSCILLATION (PIO) RATING SCALE G-1 APPENDIX H LESSONS LEARNED... H-1 Distribution List.. Inside Back Cover vii

8 LIST OF ILLUSTRATIONS Figure 1 - VEST Algorithm Integration into Test Aircraft... 2 Figure 2 - Implementation of Gain Schedule... 6 Figure 3 Implementation of Test Team Gain Schedule... 7 Figure 4 - North Velocity Error Trend with and without GPS... 8 Figure 5 North Velocity Error Trend during J-Hook Figure 6 North Position Error Trend during Long Shot Maneuver Figure 7 Average Heading Error Trend for all Sliceback Maneuvers Figure 8 - Wind Error Time History during a J-Hook Maneuver Figure 9 - Wind Error Time History during a J-Hook Maneuver Figure 10 - Wind Direction Error Time History during a Long Shot Maneuver Figure 11 - Wind Direction Error Time History during a J-Hook Maneuver Figure 12 Velocity Error Time History Figure 13 Wind Error Time History during Air-to-Air Tracking Figure 14 True Airspeed Error Time History during a J-Hook Maneuver Figure 15 Calibrated Airspeed Error for a Long Shot and J-Hook Maneuver Figure A-1 - Learjet N101VS A-1 Figure B-1 - Sliding Average Method... B-1 Figure B-2 - Representative Time History. B-2 Figure B-3 - Representative Mean Error Time History. B-4 Figure B-4 - Representative Mean Error Time History. B-5 Figure B-5 - Haar Wavelet. B-5 Figure B-6 - Haar Wavelet Resolution.. B-6 Figure B-7 - Representative Normal Probability Plot of J-Hook Coefficient Effect Estimate.. B-7 Figure B-8 - Representative Comparison of Profile Means... B-8 Figure C-1 - J-Hook Flight Test Technique... C-1 Figure C-2 - Container Flight Test Technique... C-2 Figure C-3 - Sliceback Flight Test Technique... C-3 LIST OF TABLES Table 1 - Summary of Test Flights... 1 Table 2 Average Airspeed Errors Table B-1 - Treatment Summary... B-3 Table B-2 - Representative Percentage Difference Table (J-Hook Airspeed)... B-8 Table B-3 - Summary of Significant Factors. B-8 viii

9 INTRODUCTION Background Development of the Velocity Estimate (VEST) algorithm was proposed as a student thesis research topic at the Air Force Institute of Technology. Highly augmented high performance aircraft vary control system gains as flight conditions change to preserve good handling qualities and to avoid undesirable aircraft responses. In the event of a complete air data system failure, the flight control system loses its ability to schedule gains based on changing flight conditions. In order to ensure continued safe controlled flight, standby gains are fed to the flight control computer. Typical standby gains are made up of a single airspeed and altitude value that while not optimized for current conditions, will ensure continued safe flight. The VEST algorithm was designed to provide an estimate of the lost air data information to continue optimized flight control system gain scheduling based on current flight conditions prior to necessitating the use of standby gains. The only known values available from the aircraft following the air data system failure would be the last known aircraft state prior to failure, flight control computer body axis accelerometer outputs, and flight control computer rate gyro outputs. Using this information, the estimated true airspeed would then be available for flight control system gain scheduling and for determining calibrated airspeed for display in the cockpit. Modeling and simulation to test algorithm performance was performed using facilities and resources made available by the Air Force Institute of Technology Advanced Navigation Technology Center and the Air Force Research Lab T-38 simulator at Wright Patterson Air Force Base, Ohio. Program Chronology The test program was initiated on 1 May Modification of the aircraft began on 4 June 2007 and was completed on 13 July hours of flight testing were conducted from 9 to 21 Sep A total of two ground test and six test flights were flown as shown in table 1. A detailed summary of the test points flown is presented in appendix D. Table 1 - Summary of Test Flights Ground Description /Flight 1 Ground Power-up 2 Stick Force per Stick Deflection Mapping / Taxi Test 1 Calibration Flight / Algorithm Performance Characterization 2 Algorithm Performance Characterization 3 Algorithm Performance Characterization 4 Algorithm Performance Characterization / Operational Utility Evaluation 5 Algorithm Performance Characterization / Operational Utility Evaluation 6 Algorithm Performance Characterization / Operational Utility Evaluation 1

10 Test Item Description VEST algorithm: The purpose of the VEST algorithm was to continuously estimate true airspeed following a complete air data system failure. The complete air data system failure meant that all sensors providing airspeed, altitude, temperature, angle of attack, and pressure readings were no longer available. The algorithm had three parts. The first part used available information to estimate the inertial position, velocity, and attitude. The pieces of available information were flight control computer accelerometer and rate gyro outputs, and last known position, velocity, attitude, and temperature. The algorithm used accelerometer and rate gyro outputs to propagate the last known state forward to the current state. The current state was inertial position, velocity, and attitude. The second part of the algorithm used the inertial information to continuously estimate the wind velocity. The wind was determined by the difference between the inertial track and the inertial heading to current nose position. Angle of attack and sideslip were estimated and included in the wind estimate. Finally, the true airspeed was determined by combining the inertial airspeed estimate and the wind estimate. The third part of the algorithm continuously estimated calibrated airspeed. Current temperature was estimated using a standard lapse rate based on inertial altitude deviation from last known altitude and temperature. The current temperature estimate was used to determine current pressure and density for use in converting true airspeed to calibrated airspeed. Figure 1 displays the VEST algorithm integration into the aircraft and required data inputs. Position (Latt, Long, Altitude) VEST Algorithm Learjet Velocity (North, East, Down) Attitude (Roll, Pitch, Yaw) Body (Nx, Ny, Nz) INS Velocity Attitude Position Wind KTA Body Rates (p, q, r) Temperature (Deg C) Temp Update Temp KCAS Figure 1 - VEST Algorithm Integration into Test Aircraft Test Aircraft Testing was accomplished on the Calspan VSS Learjet, N101VS incorporating a variable stability system (VSS). The modified Learjet provided in-flight simulator capability to test the VEST algorithm. The VEST algorithm was integrated onto the VSS using Matlab Simulink. The algorithm was developed as a Simulink model, and converted into an executable file to be used on the VSS. The unique characteristics of the VSS made possible real time integration of 2

11 the VEST algorithm and use of its estimated airspeed for gain scheduling. The left seat occupied by the safety pilot had basic Learjet controls and the right seat occupied by the evaluation pilot had fly-by-wire variable stability controls. If at any time the VEST algorithm produced unusable airspeed information or information that would result in an unsafe aircraft response, the VSS would disengage and give basic Learjet control back to the safety pilot. A full description of the Calspan Learjet N101VS is located in appendix A. Test Objectives The overall test objective was to evaluate the potential of the VEST algorithm in the event of a complete air data system failure. Additionally, results from testing were used to consider future VEST related tests. The specific test objectives were: Observe the Integration of the VEST Algorithm in a Ground Test Determine the Accuracy of the VEST Algorithm Inertial Speed During Taxi Determine the Airborne Accuracy of the VEST Algorithm Inertial Estimate Determine the Airborne Accuracy of the VEST Algorithm Wind Estimate Observe the Utility of the VEST Algorithm in Operational Maneuvers Determine the Airborne Accuracy of the VEST Algorithm Airspeed Estimate All test objectives were met. 3

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13 TEST AND EVALUATION General Data were collected and analyzed in accordance with the procedures outlined in appendix B. The flight test matrix for the test points used in data analysis can be found in appendix H. Integration of Velocity Estimate (VEST) Algorithm in a Ground Test The purpose of the ground test was two fold. The first task was to check the integration of VEST algorithm with the Learjet Variable Stability System (VSS) to produce required outputs. The second task was to obtain a longitudinal stick force versus control surface deflection mapping for a FCS gain schedule which could be used during the flight tests. Three power ups of the VEST algorithm implemented on the VSS from the complete power off condition were performed. VSS operation and VEST algorithm specific parameters were monitored throughout. The ground test was performed prior to first taxi. To test the utility of the VEST algorithm, a gain schedule was set up in the VSS to change the command gain. The command gain schedule fed back calibrated airspeed to set the appropriate gain. There were three possible sources of fed back calibrated airspeed: Learjet air data, VEST, and a constant value to simulate standby gains. The command gain was multiplied by the actual air data value of calibrated airspeed, referred to as a V 4 control law, then normalized by one of the three sources of fed back calibrated airspeed, referred to as a V 4 /V 4 control law. In this way, the command gain on the stick would be increased or decreased based on the value of calibrated airspeed from one of the three sources. If one of the sources provided a calibrated airspeed value that was different from the actual value, then the command gain on the stick would increase or decrease. If the fed back calibrated airspeed was the same as the actual value, then a constant command gain would result. The amount of change that would be noticeable by the pilot was set during the calibration portion of the first flight. The idea was that maneuvers would be flown in sequence using each of the three calibrated airspeed sources and compare the handling qualities observed while accomplishing specific tasks. Magnitude of airspeed errors would be perceived as changes in stick sensitivity while variations in airspeed errors would result in unpredictable aircraft responses. Figure 2 shows the implementation of this concept into the VSS. 5

14 Learjet Air Data 1.0 rec_version_havevest Standby Gains 1 delta fes (lb) vest_cmd_gain cmd_gain 2 Vc (kts) vest_vcal_ref vest_lj_vratio_exponent u v VEST vest_standby_gain_vc vest_use_standby_gain_vc 1 dec vest_use_lj_vc_2_gain_sched E_kcas 0.5t vest_vratio_exponent u v 0.5t1 Figure 2 - Implementation of Gain Schedule Stick forces (Fs) and deflections were measured before and after the calibration flight. The flight itself was performed at 15,000 feet and airspeeds of 200 to 300 KCAS to effectively calibrate the feel system for the gain scheduler. Pitch doublets, pitch captures, and rollercoaster maneuvers were performed at 220, 250, and 280 KCAS for familiarization of the basic Learjet control laws. Next a constant stick force per g (V 4 /V 4 ) was flown for pilot familiarization. Initial tests at 220 KCAS indicated a Fs/g of 4 pounds per g with a command path gain of The gain was decreased to and the resultant stick force per g was approximately 8 pounds per g. At that point, maneuvers were flown at varying airspeeds using the V 4 /V 4 control law to investigate the resulting Fs/g. The intent was to ensure the control laws were properly implemented to increase stick sensitivity as airspeed increased from 250 KCAS and became less sensitive at airspeeds less than 250 KCAS. At 250 KCAS the baseline performance as determined in the previous step was verified. All indications of system functionality prior to engine start were positive and no system errors were encountered. Normal checklist procedures required the VSS be shut-down during engine start. Once engines were started, the VEST algorithm was observed to function properly with the VSS and no significant errors were noted. Longitudinal Stick Force versus Control Surface Deflection Mapping: The plot of Fs per elevator deflection prior to and after the calibration flight is shown in figure 3 below. The slope of the plots before and after calibration matched as expected. 6

15 Baseline and Post-Calibration Comparison of Regression Coefficients First Order Coefficient of Stick Force per Stick Deflection Baseline Stick Coefficients Calibrated Airspeed (knots) 300 Calibrated Stick Coefficients Figure 3 Implementation of Test Team Gain Schedule The system integration and functional check out of the VEST algorithm onto the VSS was accomplished during the ground test. Based on the longitudinal stick force versus control surface deflection mapping comparisons, the stick force gain schedule was determined to have been implemented correctly for use on subsequent flight test evaluations. Accuracy of the VEST Algorithm Inertial Speed during Taxi Based on the results of the system integration of the VEST algorithm onto the Learjet VSS, the taxi test investigation was initiated. The purpose of the taxi test was to determine the accuracy of the VEST algorithm inertial speed estimate. The accuracy of the VEST algorithm inertial speed was determined during multiple taxi runs. The initial step performed for the taxi test was to apply tape to the Angle of Attack (Alpha) and side-slip (Beta) vanes ensuring the VSS did not trip due to excursions in Alpha and Beta during taxi. The aircraft GPS was used as the truth source for position and velocity. To verify the accuracy of the GPS, survey points along taxiway H were used as references for stationary aircraft position. The aircraft installed attitude and heading reference system (AHRS) was used as a truth source aircraft heading. The aircraft was taxied for 5 minutes and time histories of inertial speeds were recorded on the VSS for analysis. To calculate the accuracy of the VEST algorithm, inertial north, east, and down speeds were subtracted from the GPS speeds and plotted against time. This procedure was repeated both with and without GPS updates. 7

16 To evaluate the accuracy of the algorithm, north, east, and down velocity estimates were evaluated for all taxi tests with and without GPS updates. Results are presented in appendix E. Figure 4 is a sample time history plot of north velocity error with eighty percent confidence with and without GPS. 300 NORTH VELOCITY ERROR TREND Taxi Performance Comparison 200 North Velocity Error (ft/sec) Time (sec) The solid blue line represents the mean error and 80% confidence interval with GPS available. The dashed green line represents the mean error and 80% confidence interval without GPS available. Figure 4 - North Velocity Error Trend with and without GPS Post taxi test data analysis indicated that the VEST algorithm inertial speed estimate was properly integrated onboard the VSS. When GPS updates were not available, the VEST algorithm experienced drift in all three axes with no indication of correction to zero error. Results showed that the algorithm required GPS to provide an estimate to eliminate the effects of drift. Based on the error observed in the inertial speed estimate, test points without GPS updates were eliminated from flight test. Improve algorithm performance in the absence of GPS updates. (R1 1 ) 1 Numerals preceded by an R within parentheses at the end of a sentence correspond to the recommendation numbers tabulated in the Conclusions and Recommendations section of this report. 8

17 The VEST algorithm velocity errors with GPS updates were found to be on the order of 2 knots, minimally variable, and non-divergent. Therefore, follow-on airborne testing with GPS updates was justified. Airborne Accuracy of the VEST Algorithm Inertial Estimate The purpose of the inertial estimate portion of the VEST algorithm was two-fold. The inertial estimate itself was used for the calculation and display of flight information. Additionally, velocity and attitude outputs were used as inputs to the algorithm s wind estimator. The algorithm s true airspeed estimate was calculated using the inertial speed estimate and the wind estimate. Flight test techniques (FTTs) were set up to observe the accuracy of the inertial speed and heading estimates. Four separate FTTs were developed. Three of the four FTTs included turning maneuvers to provide axis observability in inertial estimates. The fourth FTT was developed to evaluate the VEST algorithm s performance during straight and level, unaccelerated flight. An explanation and description of each of the four FTTs (J-Hook, Container, Sliceback, and Long Shot) can be found in appendix C. Post flight data analysis from flights 1 and 2 indicated that the inertial estimate portion of VEST algorithm was not properly integrated with the Learjet VSS. Inertial estimates observed during flight (algorithm integration with VSS) did not match post-processed inertial estimates (algorithm integration with Simulink ). The disparity was investigated for the remainder of the flight test schedule, but was not resolved. Therefore, the airborne accuracy of the VEST algorithm s inertial estimate was determined by post-processing. North and east velocity components of the inertial estimator were evaluated. Error trends for all of the FTTs in table B-1 were similar and the error was not a function of airspeed. Additionally it was observed that the magnitude of the errors were similar in both the north and east directions. Neither aircraft maneuvers nor airspeeds affected the VEST inertial estimate error profiles. Figure 5 is a representative plot of velocity error. Results for velocity errors are presented in appendix E. 9

18 250 NORTH VELOCITY ERROR TREND J-Hook, 15,000 feet, 280 KCAS, 20 degree increment angle, 30 second dwell time, 60 degree heading change North Velocity Error (ft/sec) Time (sec) The solid line represents the mean error of all flights at these conditions. The dashed lines represent the 80% confidence interval of this mean error. Figure 5 North Velocity Error Trend during J-Hook The VEST algorithm was updated by GPS every two seconds and as such the position errors were on the order of a thousandth of a degree. The magnitude of the north and east position errors remained relatively constant throughout all of the FTTs described in appendix B and was not a function of airspeed or maneuver. Figure 6 is a representative plot of position error. Results for position errors are presented in appendix E. 10

19 0.5 NORTH POSITION ERROR TREND Long Shot, 15,000 feet, 280 KCAS North Position Error (1/1000 deg) Time (sec) The solid line represents the mean error of all flights at these conditions. The dashed lines represent the 80% confidence interval of this mean error. Figure 6 North Position Error Trend during Long Shot Maneuver The magnitude of heading errors from the VEST algorithm remained relatively constant for all of the FTTs in appendix B (as in figure 7) except for the Long Shot. The largest errors in heading of up to 150 degrees were noted during the Long Shot maneuvers. The inertial estimator was expected to drift similar to an actual INS due to the lack of aircraft accelerations in straight and level, un-accelerated flight. For all of the other FTTs, the heading error tended to zero with time, but with increasing variability. Airspeed was a significant factor in algorithm performance during the Sliceback maneuver. The higher speed test points resulted in a more desirable heading error profile (smaller magnitude and less variability). Results for heading errors are presented in appendix E. 11

20 HEADING ERROR TREND Sliceback, 15,000 feet, 220 KCAS Heading Error (deg) Time (sec) The solid line represents the mean error of all flights at these conditions. The dashed lines represent the 80% confidence interval of this mean error. Figure 7 Average Heading Error Trend for all Sliceback Maneuvers The inertial estimate errors were determined to be acceptable to use as inputs into the rest of the VEST algorithm. Further, inertial estimates for the Long Shot FTT diverged as expected. Airspeed was a significant factor in heading determination (algorithm performance at higher airspeeds was improved). Airborne Accuracy of the VEST Algorithm Wind Estimate The VEST algorithm combined ground speed (from inertial estimates) and wind speed to determine true and calibrated airspeed. The accuracy of the VEST output wind magnitude and direction were determined during this portion of the evaluation. The same four FTTs used to determine the inertial estimate accuracies were used to evaluate the airborne accuracy of the VEST algorithm wind estimate. The inputs used by the wind portion of the VEST algorithm to continuously estimate the current winds were aircraft north speed, east speed, and heading. The outputs were north and east wind components of the wind velocity. The north and east wind components were converted to magnitude (speed) and direction for comparison to Learjet provided wind truth source. A sample plot of the wind speed error trend during a J-Hook maneuver can be found in figure 8 below. The error trend plots for each of the remaining maneuvers flown can be found in appendix E. 12

21 250 WIND SPEED ERROR TREND J-Hook, 15,000 feet, 220 KCAS, 50 degree increment angle, 10 second dwell time, 150 degree heading change Wind Speed Error (kts) Time (sec) The solid line represents the mean error of all flights at these conditions. The dashed lines represent the 80% confidence interval of this mean error. Figure 8 - Wind Error Time History during a J-Hook Maneuver 250 WIND SPEED ERROR TREND J-Hook, 15,000 feet, 280 KCAS, 50 degree increment angle, 30 second dwell time, 150 degree heading change Wind Speed Error (kts) Time (sec) The solid line represents the mean error of all flights at these conditions. The dashed lines represent the 80% confidence interval of this mean error. Figure 9 - Wind Error Time History during a J-Hook Maneuver The wind speed error during the J-Hook maneuvers was found to be primarily a function of dwell time (time straight and level following a turn). Speed errors tended to increase during 13

22 turns, but decrease once the turn was complete. Errors typically reduced to less than 10 knots during a 30 second dwell time. Similar maneuvers that reduced the dwell time from 30 to 10 seconds resulted in speed errors that stayed greater than 15 knots. During the short dwell time, the wind portion of the VEST algorithm did not have enough time to determine an accurate wind speed; thus the error remained high. This analysis was conducted by a graphical comparison of 10 and 30 second dwell time J-Hook time histories, as seen in figures 8 and 9. Increment angle and total heading change were found to not be significant to the wind speed error profile. During the Long Shot maneuver, errors slowly increased with time. By graphical analysis of the Long Shot maneuvers, wind speed error divergence rate increased after approximately five minutes, see figure 10 for a representative plot WIND SPEED ERROR TREND Long Shot, 15,000 feet, 220 KCAS Wind Speed Error (kts) Time (sec) The solid line represents the mean error of all flights at these conditions. The dashed lines represent the 80% confidence interval of this mean error. Figure 10 - Wind Direction Error Time History during a Long Shot Maneuver The second portion of the wind analysis was to determine the wind direction. A sample plot of the wind direction error trend during a J-Hook maneuver can be found in figure 11 below. The error trend plots for each of the remaining maneuvers flown can be found in appendix E. 14

23 WIND DIRECTION ERROR TREND J-Hook, 15,000 feet, 220 KCAS, 20 degree increment angle, 10 second dwell time, 60 degree heading change Wind Direction Error (deg) Time (sec) The solid line represents the mean error of all flights at these conditions. The dashed lines represent the 80% confidence interval of this mean error. Figure 11 - Wind Direction Error Time History during a J-Hook Maneuver The VEST wind direction estimate was least accurate during turns. Wind direction excursions during the turning portion of the J-Hook maneuvers reached approximately 150 degrees. Once returned to a wings level attitude, errors decreased to steady values. Wind direction errors following the first turn in figure 11 were on the order of 10 degrees. After the second turn, errors increased to 15 degrees, and after the third turn, errors increased to 20 degrees. This same trend continued for the majority of J-Hook maneuvers, this analysis was conducted by a graphical comparison of time histories, as seen in figure 11. Airspeed was a significant factor in algorithm performance during the J-Hook maneuver. The higher speed test points resulted in a more desirable wind direction error profile (smaller magnitude and less variability). Similar to the Long Shot wind speed error results, the wind direction errors increased to values in excess of 90 degrees after the five minute point. The VEST wind estimate was most accurate in the wings level attitude. Estimates during turns produced unreliable values, but errors tended to decrease once the aircraft was returned to a wings level attitude. The VEST algorithm was determined invalid for providing accurate speed and direction estimates after approximately five minutes of non-maneuvering flight. Airspeed was a significant factor in wind direction determination and non-maneuver dwell time was a significant factor in wind speed determination. Algorithm performance was enhanced with nonmaneuver dwell times and higher airspeeds. 15

24 Utility of the VEST Algorithm in Operational Maneuvers The utility of the VEST Algorithm was observed during the following operationally representative maneuvers: air refueling, air-to-air and air-to-ground tracking. This was achieved by flying each of these maneuvers with three different gain schedules and comparing the corresponding aircraft response. Three gain schedules were created using fed back calibrated airspeed values from the Learjet air data system (ADS), the VEST algorithm, and 250 knots for standby gains in the V 4 /V 4 control law. Pilot comments were noted during each of the maneuvers and pilot ratings were recorded on the analog scale found in appendix D. As outlined above, the inertial estimate of the VEST algorithm was not correctly integrated onto the VSS. Outputs from the inertial estimate were key parameters in the VEST algorithm and the stick command gain schedule was based on the corresponding VEST output airspeed. Therefore, it was determined that GPS speed and AHRS heading information would feed the wind estimator portion of VEST algorithm for these real time evaluations. The post-processed average inertial speed errors were less than 5 knots of the input GPS ground speed and the heading error was less than 3 degrees of input AHRS heading. A plot showing the time history error of the difference between GPS ground speed and post processed ground speed for test point 16 on flight 5 is shown in figure 12. The near zero error profile justified the use of GPS inertial information as the inputs for the wind estimator. North Velocity Error (ft/sec) East Velocity Error (ft/sec) Vertical Velocity Error (ft/sec) VELOCITY ERROR TIME HISTORY Aerial Refueling, 15,000 feet, 280 KCAS Time (sec) Time (sec) Time (sec) Test Point and Date: 048_21_Sep Figure 12 Velocity Error Time History 16

25 Air Refueling: The maneuver started with the target stabilized on conditions (15,000 feet pressure altitude, 220/280 KCAS) and the test aircraft at a simulated observation position. The first task was to maneuver to the pre-contact position approximately 100 feet in trail. After stabilizing for 30 seconds, the test aircraft closed into the contact position, 50 feet in trail. After stabilizing for 30 seconds straight and level, the target was tracked through 90 deg of turn with 15 deg bank. ADS Gain Schedule: The control force required to produce a desired pitch response was higher than expected, but predictable. There was no delay in the pitch response. Further there was no tendency to overshoot or undershoot and typically minimal workload was encountered to obtain desired performance throughout the refueling task. No undesirable motions were noticed (Pilot in Loop Oscillation Rating (PIOR) 1). Refer to appendix G for the PIO rating scale. This performance met expectations as the V 4 /V 4 control law with ADS airspeed fed back was a constant stick force per g throughout the maneuver. VEST Gain Schedule: The control force required to produce a desired pitch response was less than the ADS gain schedule and the higher stick sensitivity was apparent. There was no noticeable delay in the pitch response and some unpredictability was noticeable during precise maneuvers in contact position. There was a mild tendency to overshoot and typically tolerable workload was encountered to obtain adequate performance throughout the refueling task. Due to the sensitivity and predictability, there was a tendency for undesirable motion to be induced easily (PIOR 3). Stick sensitivity resulted when the fed back airspeed was different from truth values. A larger error created a greater change in stick sensitivity. Unpredictability resulted from variability of error in the fed back airspeed. Standby Gain Schedule: The control force required to produce a desired pitch response was higher as compared to the previous case and the higher stick sensitivity was apparent. There was no noticeable delay in the pitch response and it was predictable. The higher control forces increase the workload and this led to task saturation. Typically high workload was encountered to obtain adequate performance throughout the refueling task. Due to the stick forces, there was a tendency for undesirable motion to be induced easily (PIOR 3). The high stick sensitivity was due to the large and fixed error in fed back airspeed. There was no variability in the fed back airspeed (due to the constant airspeed standby gain) and the aircraft response was predictable. Air-to-Air Tracking: The Learjet was equipped with an optical sight that was used during airto-air tracking. The test aircraft set up 3000 feet in trail and 1000 feet below the target. The first task was to capture the jet nozzle of the target T-38 with the upper mark of the sight. Once the capture task was complete and the aircraft were co-altitude, the next task was to track the target s canopy through 180 degrees with the target using 50 degrees of bank. During the turn the target varied pitch so as to maintain altitude within 1000 feet of the starting altitude. ADS Gain Schedule: The control force required to produce a desired pitch response was marginally high but not objectionable. There was no noticeable delay in the pitch response and it was predictable. There was no tendency to overshoot or undershoot and typically minimal workload was encountered to obtain desired performance throughout the tracking task. No undesirable motions were noticed (PIOR 1). 17

26 VEST Gain Schedule: The control force required to produce a desired pitch response was less than as compared to the previous case and the higher stick sensitivity was apparent. There was no noticeable delay in the pitch response but predictably remained in question. In one of the tracking tasks the response was highly predictable in the first 90 degrees of turn. Subsequently there was a change in the stick forces and the response became unpredictable. Despite this unpredictability, adequate performance was achieved at the cost of extensive workload. Due to the sensitivity and predictability, there was a tendency for undesirable motion to be induced easily (PIOR 3). Standby Gain Schedule: The control force required to produce a desired pitch response was higher as compared to the previous case and the higher stick sensitivity was apparent. There was no noticeable delay in the pitch response and it was predictable. The higher control forces increased the workload and this led to task saturation. Typically high workload was encountered to obtain adequate performance throughout the refueling task. Due to the stick forces, there was a tendency for undesirable motion to be induced easily (PIOR 3). Air-to-ground tracking: The Learjet s optical sight was used during air-to-ground tracking. Operationally representative ground attack maneuvers were conducted 220 and 280 KCAS for a descent of 4,000 feet. Since 20 degree dives resulted in speeds rapidly approaching 300 KCAS at idle power, shallower dive angles were used. Test points 70, 72, 74, 76, 78, and 80 were conducted by a simulated ramp delivery (straight ahead push) at the dive angle required to maintain speed. The dives were shallow, so the pilot attempted to evaluate the gain schedules by rapidly changing aim points in the dive. Recovery was conducted with a 2g level pull with mild heading changes during the climb. The control inputs required to complete these shallow angle dives were all small. The inputs were so small in fact that the pilot noticed very little difference among the three gain schedules. Minimal calibrated airspeed error was observed during the VEST test points thereby showing the ADS and VEST gain schedules to perform similarly (indistinguishable). With the standby gain schedule, flying faster than the reference airspeed (250 knots) resulted in increased stick sensitivity, while flying at lower speeds resulted in less objectionable stick sensitivity. Test points 71, 73, 75, 77, 79, and 81 were conducted by selecting a simulated target area that had multiple targets separated by approximately one mile. The test aircraft was then flown to a point roughly perpendicular to the attack axis at 200 KCAS. An aggressive roll (over bank to approximately 120 degrees) and pull (2.0g) was accomplished to aggressively capture a target on the near side of the target area. Power was reduced to idle. As airspeed increased through 220 KCAS, the aim-point was shifted to the far side of the target area (stabilizing the airspeed). Then the dive angle was aggressively steepened to a third aimpoint. As airspeed increased through 280 KCAS, a fourth target on the far side of the target area was tracked until 300 KCAS was achieved. A wings level pull to 2.0 g was used to recover followed by a heading change of approximately 90 degrees. This technique highlighted the gain schedule differences as airspeeds changed during the task of ground attack. Once again, the calibrated airspeed error observed with VEST gain scheduling was small (approximately 10 knots) and the ADS and VEST gain schedules were both assessed as desirable. The standby gain schedule, however, was not as predictable or desirable. At the slow speed roll in, the aircraft was very sluggish and difficult to change pitch attitude. At the higher speed tracking and recovery, the aircraft was extremely sensitive resulting in a stair-stepped pitch response. The tracking task became more difficult as the feel of the aircraft changed through the dive. 18

27 A sample time history plot for erratic wind errors resulting from VEST gain schedule is shown in figure 13 below. Wind Speed Error (ft/sec) WIND ERROR TIME HISTORY Air-to-Air Tracking, 15,000 feet, 220 KCAS Time (sec) Wind Direction Error (deg) Time (sec) Test Point and Date: 058_18_Sep Figure 13 Wind Error Time History during Air-to-Air Tracking The wind components directly contributed to changes in calibrated airspeed, which in turn contributed to the unpredictability in control forces based on the gain schedule. This was due to the nature of the implemented gain scheduling wherein the slope of the force change with estimation error was deliberately chosen to be steep to enable the pilot to feel small speed variations. The three operational tasks performed highlighted the capabilities and limitations of the VEST algorithm. Large errors in airspeed magnitude (more common in fed back standby gain airspeeds) resulted in stick sensitivities which adversely affected handling qualities. Large errors in airspeed variability (more common in fed back VEST airspeeds) resulted in unpredictable aircraft response which adversely affected handling qualities. Aircraft flying these operational maneuvers would typically be fighters with a speed range in excess of 600 knots. Due to the VSS envelope, the standby gain schedule was tested over a 30 knot speed range with increased stick sensitivity to simulate a wider speed range. The increased stick sensitivity was used to highlight the effect of VEST algorithm errors. The VEST algorithm demonstrated the capability to reduce the magnitude of airspeed error over standby gains (to 19

28 reduce sensitivity effect) at the cost of inducing variability. The effect of the variability was exaggerated due to the implemented gain schedule. The value of reduced sensitivity could not be evaluated. Investigate VEST algorithm performance in a less exaggerated gain schedule over wider speed envelopes. (R2) Airborne Accuracy of the VEST Algorithm Airspeed Estimate The accuracy of the VEST algorithm airspeed estimate was determined from airspeed errors between the VEST algorithm calibrated airspeed estimate and the VSS calibrated airspeed. Airspeed data from each maneuver tested were used in the analysis. VEST and VSS calibrated airspeed parameters were recorded for each maneuver. A time history of mean calibrated airspeed error bounded by its 80 percent confidence interval was plotted for each maneuver. A similar process was used to determine the accuracy of true airspeed In the inertial portion of the VEST algorithm, the inertial speed estimate (or ground speed estimate) was broken into north, east, and vertical components. The north and east speed components, along with the inertial heading, were forwarded to the wind portion of the estimator to determine the current wind speed. The north and east components of the wind speed estimate were then subtracted from the inertial speed components to satisfy the following equation for true airspeed: V T = V V. G W V T is the true velocity, V G is the ground velocity from the inertial estimate, and V W is the wind velocity. The true airspeed was then determined from the magnitude of the resulting true velocity vector. The calibrated airspeed was determined from the true airspeed and the current flight conditions from the VEST algorithm. The time history error plots for the J-Hook, Long Shot, Container, landing, and operational maneuvers were determined using post processed data. An example true airspeed error trend plot of the 220 knot J-Hook maneuver is shown in figure

29 200 TRUE AIRSPEED ERROR TREND J-Hook, 15,000 feet, 280 KCAS, 20 degree increment angle, 30 second dwell time, 60 degree heading change True Airspeed Error (ft/sec) Time (sec) The solid line represents the mean error of all flights at these conditions. The dashed lines represent the 80% confidence interval of this mean error. Figure 14 True Airspeed Error Time History during a J-Hook Maneuver Velocity error excursions were a combination of inertial and wind estimate errors. The errors were largest during the turning portion of the maneuvers, and decreased after the aircraft was returned to a wings level attitude. Error plots for the remaining maneuvers and test points can be found in appendix E. Table 2 summarizes the average errors calculated during each maneuver. Table 2 Average Airspeed Errors Maneuver Average TAS Error (ft/sec) Standard Deviation Average CAS Error (knots) Standard Deviation J-Hook Long Shot Sliceback Container Air to Air Tracking Air Refueling Air to Ground Tracking Landing Approach Individual airspeed excursions during turning portions of the maneuvers were typically in excess of the average errors shown above. The excursions were a function of both inertial and wind estimate errors, with the wind estimate providing the largest portion of the error. The largest average error determined was during the Long Shot maneuver. The primary source of error during this maneuver occurred after five minutes of non-maneuvering flight. Ground 21

30 and wind velocity estimates during the turns were as much as 150 ft per second after 15 minutes. The large errors were due to the design of the VEST algorithm. The algorithm was set up to provide airspeed estimates before and after turning maneuvers, not during the maneuvers. Nonmaneuvering flight was expected to challenge the algorithm outputs. The lowest average true airspeed error occurred during the J-Hook maneuvers. However, there was no correlation determined between maneuver type and airspeed error. The less dynamic maneuvers flown and short maneuver durations during the J-Hooks resulted in a lower overall airspeed solution estimation than during straight and level or continuous turning maneuvers. While the J-Hook maneuvers had the smallest airspeed errors, the J-Hooks also had the shortest maneuver duration. Figure 15 shows the comparison of calibrated airspeed error trends between J-Hook maneuvers and the first 90 seconds of Long shot maneuvers. 100 CALIBRATED AIRSPEED ERROR TREND Graphical comparison of Long Shot, 15,000 feet and J-Hook, 15,000 feet Flight Test Techniques Calibrated Airspeed Error (kts) Time (sec) The solid blue line represents the mean error and 80% confidence interval for the Long Shot, 15,000 feet FTT. The dashed green line represents the mean error and 80% confidence interval for the J-Hook, 15,000 feet FTT. Figure 15 Calibrated Airspeed Error for a Long Shot and J-Hook Maneuver Calibrated airspeed errors shown above are both below 5 knots. For the J-Hook maneuvers, this error was for the duration of the maneuvers whereas the Long Shot maneuvers had yet to be completed. The airborne accuracy of the VEST algorithm was determined. The average true airspeed accuracy was 12 knots (21 feet per second). The average calibrated airspeed was 10 knots (17 feet per second). The VEST airspeed estimate accuracy was independent of maneuver type. 22

31 CONCLUSIONS AND RECOMMENDATIONS The purpose of the Velocity Estimate (VEST) algorithm was to continuously estimate true airspeed following a complete air data system failure. Following air data system failure, all sensors providing airspeed, altitude, temperature, angle of attack, and pressure readings would be unavailable for use by aircraft systems. VEST provided an estimate of the lost air data information to supplement traditional standby gains with air data to schedule gains appropriate to the estimated flight condition. VEST estimated actual airspeed and flight conditions to schedule stick command gain and to display airspeed and altitude information in the cockpit. The average true airspeed error was 21 feet per second and the average calibrated airspeed error was 10 knots. The results of this test demonstrate the potential of this type of airspeed estimation as a back up system following air data failures, and warrants continued research. The results of the testing accomplished during this program are summarized below. Integration of VEST Algorithm in a Ground Test The system integration and functional check out of the VEST algorithm onto the Variable Stability System (VSS) was accomplished during the ground test. The stick force (Fs) gain schedule was determined to have been implemented correctly for use on subsequent flight test evaluations. Accuracy of the VEST Algorithm Inertial Speed during Taxi The VEST algorithm with GPS updates was found to be sufficiently accurate to continue with airborne testing. However, without GPS updates the algorithm s inertial performance was inadequate. R1: Improve algorithm performance in the absence of GPS updates. Airborne Accuracy of the VEST Algorithm Inertial Estimate The inertial estimate errors were determined to be acceptable to use as inputs into the rest of the VEST algorithm. Further, inertial estimates during long duration straight and level flight diverged as expected. Airspeed was a significant factor in heading determination (algorithm performance at higher airspeeds was improved). Airborne Accuracy of the VEST Algorithm Wind Estimate The VEST wind estimate was most accurate in the wings level attitude. Estimates during turns produced unreliable values, but errors tended to decrease once the aircraft was returned to a wings level attitude. The VEST algorithm was determined invalid for providing accurate speed and direction estimates after approximately five minutes of non-maneuvering flight. Airspeed was a significant factor in wind direction determination and non-maneuver dwell time was a significant factor in wind speed determination. Algorithm performance was enhanced with nonmaneuver dwell times and higher airspeeds. Utility of the VEST Algorithm in Operational Maneuvers Three operational tasks highlighted the capabilities and limitations of the VEST algorithm. Large airspeed magnitude errors (more common in fed back standby gain airspeeds) resulted in 23

32 stick sensitivities which adversely affected handling qualities. Large airspeed variability errors (more common in fed back VEST airspeeds) resulted in unpredictable aircraft response which adversely affected handling qualities. Aircraft flying these operational maneuvers would typically be fighters with a speed range in excess of 600 knots. Due to the VSS envelope, the standby gain schedule was tested over a 30 knot speed range with increased stick sensitivity to simulate a wider speed range. The increased stick sensitivity was used to highlight the effect of VEST algorithm errors. The VEST algorithm demonstrated the capability to reduce the magnitude of airspeed error over standby gains (to reduce sensitivity effect) at the cost of inducing variability. The effect of the variability was exaggerated due to the implemented gain schedule. R2: Investigate VEST algorithm performance in a less exaggerated gain schedule over wider speed envelopes. Airborne Accuracy of the VEST Algorithm Airspeed Estimate The airborne accuracy of the VEST algorithm was determined. The average true airspeed accuracy was 12 knots (21 feet per second). The average calibrated airspeed was 10 knots (17 feet per second). The VEST airspeed estimate accuracy was independent of maneuver type. The airspeed error magnitude and variability affect the handling qualities of a highly augmented aircraft. The VEST algorithm has been demonstrated to reduce the error magnitude over standby gains, but increase the error variability (increase unpredictability). Potential exists for future applications with VEST. 24

33 REFERENCES 1. Montgomery, D. C. (2005). Design and Analysis of Experiments, 6 th Edition. John Wiley & Sons, Inc., Hobucken, NJ. 2. Addison, P.S. (2002). The Illustrated Wavelet Transform Handbook, Introductory Theory and Applications in Science, Engineering, Medicine, and Finance. Institute of Physics Publishing, Ltd., Philadelphia, PA. 3. McLaren, S.A. (2008). Airspeed Estimate Following Air Data System Failure. Air Force University Press, Maxwell AFB, AL. 4. Calspan Flight Research Group (2006). Learjet Flight Syllabus and Background Material for the USAF/USN Test Pilot School Variable Stability Programs. Niagara Falls, NY. 25

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35 APPENDIX A DETAILED TEST ARTICLE DESCRIPTION Figure A-1 Learjet N101VS The Calspan Learjet LJ-24, N101VS was used exclusively for this test program (reference 4). Variable Stability Learjet N101VS: The Calspan Variable Stability Learjet was a modified Learjet designed to serve as a three axis in-flight simulator, where normal operations included the use of a safety pilot and an evaluation pilot. The safety pilot s controls (left seat) were standard, but the evaluation pilot s controls (right seat) were replaced with components of fly-bywire, response feedback, variable stability, and variable control systems. The response feedback flight control system used the Learjet control surfaces to augment the stability characteristics of the basic Learjet. Variable Stability System (VSS): The VSS was divided into two independent parts, a variable feel system and a response feedback system. The variable feel system provided the evaluation pilot with the stick and rudder pedal forces, gradients, and displacements, while the response feedback flight control system augmented the normal Learjet dynamics to represent those of the vehicle being simulated. The evaluation pilot s inputs were fed into the flight control system through the feel system, and the resulting control surface movements produced the aircraft response. The loop was closed by sensing the aircraft s motions and feeding back signals proportional to these motions, thus modifying the response to the pilot s inputs. Angle of attack vanes, sideslip vanes, rate and attitude gyros, and air data information were all used as the sensor elements. The VSS flight control modes were as follows: VSS MODE: For purposes of this test, this was set to the basic aircraft parameters. A modified stick-command gain was scheduled in the speed range between 200 and 300 knots, in order to highlight estimated airspeed errors. Existing safety trips were not affected and remained in place. EMERGENCY FLY BY WIRE (FBW) MODE: In the event the safety pilot becomes incapacitated or certain control cable failures occurred, the evaluation pilot can fly the aircraft as a normal Learjet using the FBW mode. All basic Learjet systems (gear, A-1